Author name cluster

Robert Mattmüller

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29 papers

2 author rows

ICAPS Conference 2022 Conference Paper

Loopless Top-K Planning

Julian von Tschammer
Robert Mattmüller
David Speck 0001

In top-k planning, the objective is to determine a set of k cheapest plans that provide several good alternatives to choose from. Such a solution set often contains plans that visit at least one state more than once. Depending on the application, plans with such loops are of little importance because they are dominated by a loopless representative and can prevent more meaningful plans from being found. In this paper, we motivate and introduce loopless top-k planning. We show how to enhance the state-of-the-art symbolic top-k planner, symK, to obtain an efficient, sound and complete algorithm for loopless top-k planning. An empirical evaluation shows that our proposed approach has a higher k-coverage than a generate-and-test approach that uses an ordinary top-k planner, which we show to be incomplete in the presence of zero-cost loops.

AIJ Journal 2021 Journal Article

Game description language and dynamic epistemic logic compared

Thorsten Engesser
Robert Mattmüller
Bernhard Nebel
Michael Thielscher

Several different frameworks have been proposed to model and reason about knowledge in dynamic multi-agent settings, among them the logic-programming-based game description language GDL-III and dynamic epistemic logic (DEL). GDL-III and DEL have complementary strengths and weaknesses in terms of ease of modeling and simplicity of semantics. In this paper, we formally study the expressiveness of GDL-III vs. DEL. We clarify the commonalities and differences between those languages, demonstrate how to bridge the differences where possible, and identify large fragments of GDL-III and DEL that are equivalent in the sense that they can be used to encode games or planning tasks that admit the same legal action sequences. We prove the latter by providing translations between those fragments of GDL-III and DEL.

ICAPS Conference 2021 Conference Paper

Learning Heuristic Selection with Dynamic Algorithm Configuration

David Speck 0001
André Biedenkapp
Frank Hutter
Robert Mattmüller
Marius Lindauer

A key challenge in satisficing planning is to use multiple heuristics within one heuristic search. An aggregation of multiple heuristic estimates, for example by taking the maximum, has the disadvantage that bad estimates of a single heuristic can negatively affect the whole search. Since the performance of a heuristic varies from instance to instance, approaches such as algorithm selection can be successfully applied. In addition, alternating between multiple heuristics during the search makes it possible to use all heuristics equally and improve performance. However, all these approaches ignore the internal search dynamics of a planning system, which can help to select the most useful heuristics for the current expansion step. We show that dynamic algorithm configuration can be used for dynamic heuristic selection which takes into account the internal search dynamics of a planning system. Furthermore, we prove that this approach generalizes over existing approaches and that it can exponentially improve the performance of the heuristic search. To learn dynamic heuristic selection, we propose an approach based on reinforcement learning and show empirically that domain-wise learned policies, which take the internal search dynamics of a planning system into account, can exceed existing approaches.

ICAPS Conference 2021 Conference Paper

On the Compilability and Expressive Power of State-Dependent Action Costs

David Speck 0001
David Borukhson
Robert Mattmüller
Bernhard Nebel

While state-dependent action costs are practically relevant and have been studied before, it is still unclear if they are an essential feature of planning tasks. In this paper, we study to what extent state-dependent action costs are an essential feature by analyzing under which circumstances they can be compiled away. We give a complete classification for all combinations of action cost functions and possible cost measures for the compilations. Our theoretical results show that if both task sizes and plan lengths are to be preserved polynomially, then the boundary between compilability and non-compilability lies between FP and FPSPACE computable action cost functions (under a mild assumption on the polynomial hierarchy). Preserving task sizes polynomially and plan lengths linearly at the same time is impossible.

AIJ Journal 2020 Journal Article

Evaluation of the moral permissibility of action plans

Felix Lindner
Robert Mattmüller
Bernhard Nebel

Research in classical planning so far has been mainly concerned with generating a satisficing or an optimal plan. However, if such systems are used to make decisions that are relevant to humans, one should also consider the ethical consequences generated plans can have. Traditionally, ethical principles are formulated in an action-based manner, allowing to judge the execution of one action. We show how such a judgment can be generalized to plans. Further, we study the computational complexity of making ethical judgment about plans.

PRL Workshop 2020 Workshop Paper

Learning Heuristic Selection with Dynamic Algorithm Configuration

David Speck
André Biedenkapp
Frank Hutter
Robert Mattmüller
Marius Lindauer

A key challenge in satisficing planning is to use multiple heuristics within one heuristic search. An aggregation of multiple heuristic estimates, for example by taking the maximum, has the disadvantage that bad estimates of a single heuristic can negatively affect the whole search. Since the performance of a heuristic varies from instance to instance, approaches such as algorithm selection can be successfully applied. In addition, alternating between multiple heuristics during the search makes it possible to use all heuristics equally and improve performance. However, all these approaches ignore the internal search dynamics of a planning system, which can help to select the most helpful heuristics for the current expansion step. We show that dynamic algorithm configuration can be used for dynamic heuristic selection which takes into account the internal search dynamics of a planning system. Furthermore, we prove that this approach generalizes over existing approaches and that it can exponentially improve the performance of the heuristic search. To learn dynamic heuristic selection, we propose an approach based on reinforcement learning and show empirically that domain-wise learned policies, which take the internal search dynamics of a planning system into account, can exceed existing approaches in terms of coverage.

AAAI Conference 2020 Conference Paper

Symbolic Top-k Planning

David Speck
Robert Mattmüller
Bernhard Nebel

The objective of top-k planning is to determine a set of k different plans with lowest cost for a given planning task. In practice, such a set of best plans can be preferred to a single best plan generated by ordinary optimal planners, as it allows the user to choose between different alternatives and thus take into account preferences that may be difﬁcult to model. In this paper we show that, in general, the decision problem version of top-k planning is PSPACE-complete, as is the decision problem version of ordinary classical planning. This does not hold for polynomially bounded plans for which the decision problem turns out to be PP-hard, while the ordinary case is NP-hard. We present a novel approach to top-k planning, called SYM-K, which is based on symbolic search, and prove that SYM-K is sound and complete. Our empirical analysis shows that SYM-K exceeds the current state of the art for both small and large k.

KR Conference 2020 Conference Paper

Token-based Execution Semantics for Multi-Agent Epistemic Planning

Thorsten Engesser
Robert Mattmüller
Bernhard Nebel
Felicitas Ritter

Epistemic planning has been employed as a means to achieve implicit coordination in cooperative multi-agent systems where world knowledge is distributed between the agents, and agents plan and act individually. However, recent work has shown that even if all agents act with respect to plans that they consider optimal from their own subjective perspective, infinite executions can occur. In this paper, we analyze the idea of using a single token that can be passed around between the agents and which is used as a prerequisite for acting. We show that introducing such a token to any planning task will prevent the existence of infinite executions. We furthermore analyze the conditions under which solutions to a planning task are preserved under our tokenization.

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ICAPS Conference 2020 Conference Paper

When Perfect Is Not Good Enough: On the Search Behaviour of Symbolic Heuristic Search

David Speck 0001
Florian Geißer
Robert Mattmüller

Symbolic search has proven to be a competitive approach to cost-optimal planning, as it compactly represents sets of states by symbolic data structures. While heuristics for symbolic search exist, symbolic bidirectional blind search empirically outperforms its heuristic counterpart and is therefore the dominant search strategy. This prompts the question of why heuristics do not seem to pay off in symbolic search. As a first step in answering this question, we investigate the search behaviour of symbolic heuristic search by means of BDDA⋆. Previous work identified the partitioning of state sets according to their heuristic values as the main bottleneck. We theoretically and empirically evaluate the search behaviour of BDDA⋆ and reveal another fundamental problem: we prove that the use of a heuristic does not always improve the search performance of BDDA⋆. In general, even the perfect heuristic can exponentially deteriorate search performance.

JAIR Journal 2019 Journal Article

Implicitly Coordinated Multi-Agent Path Finding under Destination Uncertainty: Success Guarantees and Computational Complexity

Bernhard Nebel
Thomas Bolander
Thorsten Engesser
Robert Mattmüller

In multi-agent path finding (MAPF), it is usually assumed that planning is performed centrally and that the destinations of the agents are common knowledge. We will drop both assumptions and analyze under which conditions it can be guaranteed that the agents reach their respective destinations using implicitly coordinated plans without communication. Furthermore, we will analyze what the computational costs associated with such a coordination regime are. As it turns out, guarantees can be given assuming that the agents are of a certain type. However, the implied computational costs are quite severe. In the distributed setting, we either have to solve a sequence of NP-complete problems or have to tolerate exponentially longer executions. In the setting with destination uncertainty, bounded plan existence becomes PSPACE-complete. This clearly demonstrates the value of communicating about plans before execution starts.

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IJCAI Conference 2019 Conference Paper

Implicitly Coordinated Multi-Agent Path Finding under Destination Uncertainty: Success Guarantees and Computational Complexity (Extended Abstract)

Bernhard Nebel
Thomas Bolander
Thorsten Engesser
Robert Mattmüller

In multi-agent path finding, it is usually assumed that planning is performed centrally and that the destinations of the agents are common knowledge. We will drop both assumptions and analyze under which conditions it can be guaranteed that the agents reach their respective destinations using implicitly coordinated plans without communication.

AAAI Conference 2019 Conference Paper

Moral Permissibility of Action Plans

Felix Lindner
Robert Mattmüller
Bernhard Nebel

Research in classical planning so far was mainly concerned with generating a satisficing or an optimal plan. However, if such systems are used to make decisions that are relevant to humans, one should also consider the ethical consequences generated plans can have. We address this challenge by analyzing in how far it is possible to generalize existing approaches of machine ethics to automatic planning systems. Traditionally, ethical principles are formulated in an actionbased manner, allowing to judge the execution of one action. We show how such a judgment can be generalized to plans. Further, we study the computational complexity of making ethical judgment about plans.

ICAPS Conference 2019 Conference Paper

Symbolic Planning with Axioms

David Speck 0001
Florian Geißer
Robert Mattmüller
Álvaro Torralba

Axioms are an extension for classical planning models that allow for modeling complex preconditions and goals exponentially more compactly. Although axioms were introduced in planning more than a decade ago, modern planning techniques rarely support axioms, especially in cost-optimal planning. Symbolic search is a popular and competitive optimal planning technique based on the manipulation of sets of states. In this work, we extend symbolic search algorithms to support axioms natively. We analyze different ways of encoding derived variables and axiom rules to evaluate them in a symbolic representation. We prove that all encodings are sound and complete, and empirically show that the presented approach outperforms the previous state of the art in costoptimal classical planning with axioms.

JELIA Conference 2019 Conference Paper

The Dynamic Logic of Policies and Contingent Planning

Thomas Bolander
Thorsten Engesser
Andreas Herzig
Robert Mattmüller
Bernhard Nebel

Abstract In classical deterministic planning, solutions to planning tasks are simply sequences of actions, but that is not sufficient for contingent plans in non-deterministic environments. Contingent plans are often expressed through policies that map states to actions. An alternative is to specify contingent plans as programs, e. g. in the syntax of Propositional Dynamic Logic (PDL). PDL is a logic for reasoning about programs with sequential composition, test and non-deterministic choice. However, as we show in the paper, none of the existing PDL modalities directly captures the notion of a solution to a planning task under non-determinism. We add a new modality to star-free PDL correctly capturing this notion. We prove the appropriateness of the new modality by showing how to translate back and forth between policies and PDL programs under the new modality. More precisely, we show how a policy solution to a planning task gives rise to a program solution expressed via the new modality, and vice versa. We also provide an axiomatisation of our PDL extension through reduction axioms into standard star-free PDL.

KR Conference 2018 Conference Paper

Better Eager Than Lazy? How Agent Types Impact the Successfulness of Implicit Coordination

Thomas Bolander
Thorsten Engesser
Robert Mattmüller
Bernhard Nebel

Epistemic planning can be used for decision making in multiagent situations with distributed knowledge and capabilities. In recent work, we proposed a new notion of strong policies with implicit coordination. With this it is possible to solve planning tasks with joint goals from a single-agent perspective without the agents having to negotiate about and commit to a joint policy at plan time. We study how and under which circumstances the decentralized application of those policies leads to the desired outcome.

KR Conference 2018 Conference Paper

Compiling Away Soft Trajectory Constraints in Planning

Benedict Wright
Robert Mattmüller
Bernhard Nebel

Soft goals in planning are optional objectives that should be achieved in the terminal state. However, failing to achieve them does not result in the plan becoming invalid. State trajectory constraints are hard requirements towards the state trajectory of the plan. Soft trajectory constraints are a combination of both: soft preferences on how the hard goals are reached, i. e. , optional requirements towards the state trajectory of the plan. Such a soft trajectory constraint may require that some fact should be always true, or should be true at some point during the plan. The quality of a plan is then measured by a metric which adds the sum of all action costs and a penalty for each failed soft trajectory constraint. Keyder and Geffner showed that soft goals can be compiled away. We generalize this approach and illustrate a method of compiling soft trajectory constraints into conditional effects and state dependent action costs using LTLf and deterministic finite automata. We provide two compilation schemes, with and without reward shaping, by rewarding and penalizing different states in the plan. With this we are able to handle such soft trajectory constraints without the need of altering the search algorithm or heuristics, using classical planners.

IJCAI Conference 2018 Conference Paper

Game Description Language and Dynamic Epistemic Logic Compared

Thorsten Engesser
Robert Mattmüller
Bernhard Nebel
Michael Thielscher

Several different frameworks have been proposed to model and reason about knowledge in dynamic multi-agent settings, among them the logic-programming-based game description language GDL-III, and dynamic epistemic logic (DEL), based on possible-worlds semantics. GDL-III and DEL have complementary strengths and weaknesses in terms of ease of modeling and simplicity of semantics. In this paper, we formally study the expressiveness of GDL-III vs. DEL. We clarify the commonalities and differences between those languages, demonstrate how to bridge the differences where possible, and identify large fragments of GDL-III and DEL that are equivalent in the sense that they can be used to encode games or planning tasks that admit the same legal action sequences. We prove the latter by providing compilations between those fragments of GDL-III and DEL.

AAAI Conference 2018 Conference Paper

On the Relationship Between State-Dependent Action Costs and Conditional Effects in Planning

Robert Mattmüller
Florian Geißer
Benedict Wright
Bernhard Nebel

When planning for tasks that feature both state-dependent action costs and conditional effects using relaxation heuristics, the following problem appears: handling costs and effects separately leads to worse-than-necessary heuristic values, since we may get the more useful effect at the lower cost by choosing different values of a relaxed variable when determining relaxed costs and relaxed active effects. In this paper, we show how this issue can be avoided by representing state-dependent costs and conditional effects uniformly, both as edge-valued multi-valued decision diagrams (EVMDDs) over different sets of edge values, and then working with their product diagram. We develop a theory of EVMDDs that is general enough to encompass state-dependent action costs, conditional effects, and even their combination. We deﬁne relaxed effect semantics in the presence of statedependent action costs and conditional effects, and describe how this semantics can be efﬁciently computed using product EVMDDs. This will form the foundation for informative relaxation heuristics in the setting with state-dependent costs and conditional effects combined.

ICAPS Conference 2018 Conference Paper

Symbolic Planning with Edge-Valued Multi-Valued Decision Diagrams

David Speck 0001
Florian Geißer
Robert Mattmüller

Symbolic representations have attracted significant attention in optimal planning. Binary Decision Diagrams (BDDs) form the basis for symbolic search algorithms. Closely related are Algebraic Decision Diagrams (ADDs), used to represent heuristic functions. Also, progress was made in dealing with models that take state-dependent action costs into account. Here, costs are represented as Edge-valued Multi-valued Decision Diagrams (EVMDDs), which can be exponentially more compact than the corresponding ADD representation. However, they were not yet considered for symbolic planning. In this work, we study EVMDD-based symbolic search for optimal planning. We define EVMDD-based representations of state sets and transition relations, and show how to compute the necessary operations required for EVMDD-A*. This EVMDD-based version of symbolic A* generalizes its BDD variant, and allows to solve planning tasks with state-dependent action costs. We prove theoretically that our approach is sound, complete and optimal. Additionally, we present an empirical analysis comparing EVMDD-A* to BDD-A* and explicit A* search. Our results underscore the usefulness of symbolic approaches and the feasibility of dealing with models that go beyond unit costs.

ICAPS Conference 2016 Conference Paper

Abstractions for Planning with State-Dependent Action Costs

Florian Geißer
Thomas Keller 0001
Robert Mattmüller

Extending the classical planning formalism with state-dependent action costs (SDAC) allows an up to exponentially more compact task encoding. Recent work proposed to use edge-valued multi-valued decision diagrams (EVMDDs) to represent cost functions, which allows to automatically detect and exhibit structure in cost functions and to make heuristic estimators accurately reflect SDAC. However, so far only the inadmissible additive heuristic has been considered in this context. In this paper, we define informative admissible abstraction heuristics which enable optimal planning with SDAC. We discuss how abstract cost values can be extracted from EVMDDs that represent concrete cost functions without adjusting them to the selected abstraction. Our theoretical analysis shows that this is efficiently possible for abstractions that are Cartesian or coarser. We adapt the counterexample-guided abstraction refinement approach to derive such abstractions. An empirical evaluation of the resulting heuristic shows that highly accurate values can be computed quickly.

SoCS Conference 2015 Conference Paper

Delete Relaxations for Planning with State-Dependent Action Costs

Florian Geißer
Thomas Keller 0001
Robert Mattmüller

Supporting state-dependent action costs in planning admits a more compact representation of many tasks. We generalize the additive heuristic and compute it by embedding decision-diagram representations of action cost functions into the RPG. We give a theoretical evaluation and present an implementation of the generalized additive heuristic. This allows us to handle even the hardest instances of the combinatorial Academic Advising domain from the IPPC 2014.

ECAI Conference 2014 Conference Paper

Past, Present, and Future: An Optimal Online Algorithm for Single-Player GDL-II Games

Florian Geißer
Thomas Keller 0001
Robert Mattmüller

In General Game Playing, a player receives the rules of an unknown game and attempts to maximize his expected reward. Since 2011, the GDL-II rule language extension allows the formulation of nondeterministic and partially observable games. In this paper, we present an algorithm for such games, with a focus on the single-player case. Conceptually, at each stage, the proposed NORNS algorithm distinguishes between the past, present and future steps of the game. More specifically, a belief state tree is used to simulate a potential past that leads to a present that is consistent with received observations. Unlike other related methods, our method is asymptotically optimal. Moreover, augmenting the belief state tree with iteratively improved probabilities speeds up the process over time significantly.

ICAPS Conference 2013 Conference Paper

The Relative Pruning Power of Strong Stubborn Sets and Expansion Core

Martin Wehrle
Malte Helmert
Yusra Alkhazraji
Robert Mattmüller

In the last years, pruning techniques based on partial order reduction have found increasing attention in the planning community. One recent result is that the expansion core method is a special case of the strong stubborn sets method proposed in model checking. However, it is still an open question if there exist efficiently computable strong stubborn sets with strictly higher pruning power than expansion core. In this paper, we prove that the pruning power of strong stubborn sets is strictly higher than the pruning power of expansion core even for a straight-forward instantiation of strong stubborn sets. This instantiation is as efficiently computable as expansion core. Hence, our theoretical results suggest that strong stubborn sets should be preferred to expansion core. Our empirical evaluation on all optimal benchmarks from the international planning competitions up to 2011 supports the theoretical results.

ECAI Conference 2012 Conference Paper

A Stubborn Set Algorithm for Optimal Planning

Yusra Alkhazraji
Martin Wehrle
Robert Mattmüller
Malte Helmert

We adapt a partial order reduction technique based on stubborn sets, originally proposed for detecting dead ends in Petri Nets, to the setting of optimal planning. We demonstrate that stubborn sets can provide significant state space reductions on standard planning benchmarks, outperforming the expansion core method.

ICAPS Conference 2010 Conference Paper

G-Value Plateaus: A Challenge for Planning

J. Benton 0001
Kartik Talamadupula
Patrick Eyerich
Robert Mattmüller
Subbarao Kambhampati

While the string of successes found in using heuristic, best-first search methods have provided positive reinforcement for continuing work along these lines, fundamental problems arise when handling objectives whose value does not change with search operations. An extreme case of this occurs when handling the objective of generating a temporal plan with short makespan. Typically used heuristic search methods assume strictly positive edge costs for their guarantees on completeness and optimality, while the usual ``fattening'' and ``advance time'' steps of heuristic search for temporal planning have the potential of resulting in ``g-value plateaus''. In this paper we point out some underlying difficulties with using modern heuristic search methods when operating over g-value plateaus and discuss how the presence of these problems contributes to the poor performance of heuristic search planners. To further illustrate this, we show empirical results on recent benchmarks using a planner made with makespan optimization in mind.

ICAPS Conference 2010 Conference Paper

Pattern Database Heuristics for Fully Observable Nondeterministic Planning

Robert Mattmüller
Manuela Ortlieb
Malte Helmert
Pascal Bercher

When planning in an uncertain environment, one is often interested in finding a contingent plan that prescribes appropriate actions for all possible states that may be encountered during the execution of the plan. We consider the problem of finding strong cyclic plans for fully observable nondeterministic (FOND) planning problems. The algorithm we choose is LAO*, an informed explicit state search algorithm. We investigate the use of pattern database (PDB) heuristics to guide LAO* towards goal states. To obtain a fully domain-independent planning system, we use an automatic pattern selection procedure that performs local search in the space of pattern collections. The evaluation of our system on the FOND benchmarks of the Uncertainty Part of the International Planning Competition 2008 shows that our approach is competitive with symbolic regression search in terms of problem coverage, speed, and plan quality.

ICAPS Conference 2009 Conference Paper

Using the Context-enhanced Additive Heuristic for Temporal and Numeric Planning

Patrick Eyerich
Robert Mattmüller
Gabriele Röger

Planning systems for real-world applications need the ability to handle concurrency and numeric fluents. Nevertheless, the predominant approach to cope with concurrency followed by the most successful participants in the latest International Planning Competitions (IPC) is still to find a sequential plan that is rescheduled in a post-processing step. We present Temporal Fast Downward (TFD), a planning system for temporal problems that is capable of finding low-makespan plans by performing a heuristic search in a temporal search space. We show how the context-enhanced additive heuristic can be successfully used for temporal planning and how it can be extended to numeric fluents. TFD often produces plans of high quality and, evaluated according to the rating scheme of the last IPC, outperforms all state-of-the-art temporal planning systems.

ECAI Conference 2008 Conference Paper

A Planning Graph Heuristic for Forward-Chaining Adversarial Planning

Pascal Bercher
Robert Mattmüller

In contrast to classical planning, in adversarial planning, the planning agent has to face an adversary trying to prevent him from reaching his goals. In this paper, we investigate a forwardchaining approach to adversarial planning based on the AO*algorithm. The exploration of the underlying AND/OR graph is guided by a heuristic evaluation function, inspired by the relaxed planning graph heuristic used in the FF planner. Unlike FF, our heuristic uses an adversarial planning graph with distinct proposition and action layers for the protagonist and antagonist. First results suggest that in certain planning domains, our approach yields results competitive with the state of the art.

ECAI Conference 2006 Conference Paper

Aproximation Properties of Planning Benchmarks

Malte Helmert
Robert Mattmüller
Gabriele Röger

For many classical planning domains, the computational complexity of non-optimal and optimal planning is known. However, little is known about the area in between the two extremes of finding some plan and finding optimal plans. In this contribution, we provide a complete classification of the propositional domains from the first four International Planning Competitions with respect to the approximation classes PO, PTAS, APX, poly-APX, and NPO.